Solve for $x$ and $y$ by deriving an expression for $y$ from the second equation, and substituting it back into the first equation. $\begin{align*}6x+3y &= -3 \\ 5x-3y &= -3\end{align*}$
Explanation: Begin by moving the $x$ -term in the second equation to the right side of the equation. $-3y = -5x-3$ Divide both sides by $-3$ to isolate $y$ $y = {\dfrac{5}{3}x + 1}$ Substitute this expression for $y$ in the first equation. $6x+3({\dfrac{5}{3}x + 1}) = -3$ $6x + 5x + 3 = -3$ Simplify by combining terms, then solve for $x$ $11x + 3 = -3$ $11x = -6$ $x = -\dfrac{6}{11}$ Substitute $-\dfrac{6}{11}$ for $x$ back into the top equation. $6( -\dfrac{6}{11})+3y = -3$ $-\dfrac{36}{11}+3y = -3$ $3y = \dfrac{3}{11}$ $y = \dfrac{1}{11}$ The solution is $\enspace x = -\dfrac{6}{11}, \enspace y = \dfrac{1}{11}$.